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Topic review (newest first)
- jacks
- 2012-12-15 15:03:36
Thanks Bobbundy Got it.
- bob bundy
- 2012-12-14 07:20:52
Ok. Let's say P is (a,b) Q is (c,d) and R is (e,f)
a,b,c,d,e and f are all rational ie they are fractions
Midpoint PQ
and centroid is
the {rationals} are closed for +, - , x and ÷
ie. adding two fractions, or subtracting one fraction from another, or multiplying two fractions or dividing them will always give another fracftion.
Therefore both the midpoint and the centroid have rational coordinates.
Bob
- jacks
- 2012-12-14 06:56:45
Thanks bob bundy
but I did not understand the meaning of the Given line
R is also rational so the point one third of the way up from PQ towards R will be rational
- bob bundy
- 2012-12-14 03:11:27
hi jacks
Hhhmmm. This is a new problem for me. But I suppose you could tackle it like this:
centroid: is at the intersection of the medians (which join the midpoint of a side to the opposite vertex, and is also one third of the way up any median.
So if P and Q have rational coordinates so will the midpoint of PQ.
R is also rational so the point one third of the way up from PQ towards R will be rational.
How does that sound to you?
Bob
- jacks
- 2012-12-13 22:43:32
if the vertices P, Q, R of a triangle PQR are rational points
Then which of the following points is(are) always rational point(s)
options.
(a)centroid (b)incentre (c)orthocentre (d)circumcentreplz explain answer